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The Annular Groove Phase Mask (AGPM) is a vectorial vortex phase mask. Itacts as a half-wave plate with a radial fast axis orientation operating in themid infrared domain. When placed at the focus of a telescope element provides acontinuous helical phase ramp for an on axis sources, which creates the orbitalangular momentum. Thanks to that phase, the intensity of the central source iscanceled by a down-stream pupil stop, while the off axis sources are notaffected. However due to experimental conditions the nulling is hardly perfect.To improve the null, a Mach-Zehnder interferometer containing Dove prismsdifferently oriented can be proposed to sort out light based on its orbitalangular momentum (OAM). Thanks to the differential rotation of the beam, a{\pi} phase shift is achieved for the on axis light affected by a non zero OAM.Therefore the contrast between the star and its faint companion is enhanced.Nevertheless, due the Dove prisms birefringence, the performance of theinterferometer is relatively poor. To solve this problem, we propose to add abirefringent wave-plate in each arm to compensate this birefringence. In thispaper, we will develop the mathematical model of the wave front using the Jonesformalism. The performance of the interferometer is at first computed for thesimple version without the birefringent plate. Then the effect of thebirefringent plate is be mathematically described and the performance isre-computed.

A Mach-Zehnder interferometer based on orbital angular momentum for improved vortex coronagraph efficiency